Borbala Gerhat

I am currently an MSCA Fellow at the Institute of Science and Technology Austria (AT) under the supervision of Prof. Robert Seiringer.

Research interests

Functional analysis, (non-self-adjoint) operator and spectral theory, operator families, operator matrices, PDEs, generalised form methods, representation theorems, Schrödinger operators, discrete Hardy type inequalities

Publications

1. Criticality transition for positive powers of the discrete Laplacian on the half line
   Revista Matemática Iberoamericana (2025)
   (with D. Krejčiřík and F. Štampach, arXiv)

2. An improved discrete Rellich inequality on the half-line
   Israel Journal of Mathematics (to appear)
   (with D. Krejčiřík and F. Štampach, arXiv)

3. Schur complement dominant operator matrices
   Journal of Functional Analysis (2024) Vol. 286, No. 110195
   (arXiv)

4. On the point spectrum in the Ekman boundary layer problem
   Communications in Mathematical Physics (2022) Vol. 392, p. 377-397
   (with O. O. Ibrogimov and P. Siegl)

5. Pseudo numerical ranges and spectral enclosures
   Complex Analysis and Operator Theory (2022) Vol. 16, No. 78
   (with C. Tretter, arXiv)

6. Schrödinger operators with accretive potentials in weighted spaces
   (with P. Siegl, preprint)

7. Semigroup decay for wave equations with damping coefficient unbounded at infinity
   (with A. Arnal, J. Royer and P. Siegl, preprint)

Invited conference talks

• RSME's 7th Congress of Young Researchers - Dispersive Equations and Spectral Theory
  Jan 2025, Universidad del País Vasco, Bilbao (ES)
  Energy decay for strongly damped wave equations

• YRFAMP at WOTCA 2024
  Jul 2024, Universidade da Madeira, Funchal (PT)
  Energy decay for strongly damped wave equations

• Spectral and Scattering Theory
  Jun 2024, Université Paul Sabatier, Toulouse (FR)
  Energy decay for strongly damped wave equations

• Analytic and algebraic methods in physics
  Aug 2023, Czech Technical University in Prague (CZ)
  Powers of discrete Laplacians and Hardy-type inequalities

• YRFAMP at WOTCA 2023
  Jul 2023, Universidade de Évora (PT)
  Criticality analysis of powers of the discrete Laplacian

• Challenges in Spectral Theory of Differential Operators
  Dec 2022, Graz University of Technology (AT)
  Schrödinger operators with accretive potentials in weighted spaces

• Mathematical aspects of the physics with non-self-adjoint operators
  Jul 2022, Banff International Research Station (CA)
  Schur complement dominance with applications to damped wave equations

• YRFAMP at WOTCA 2022
  Jun 2022, Universidade do Algarve, Faro (PT)
  Pseudo numerical ranges

• Challenges in Non-self-adjoint Spectral Theory
  Dec 2019, Queen's University Belfast (UK)
  Schur complement dominant operator matrices

• 6. Weihnachtskolloquium
  Dec 2017, Vienna University of Technology (AT)
  Quadratic numerical range and spectral enclosure

Selected contributed talks / seminars

• Workshop X Partial differential equations, optimal design and numerics
  Aug 2024, Centro de Sciencias de Benasque Pedro Pascual (ES)
  Energy decay for strongly damped wave equations

• Mathematical aspects of the physics with non-self-adjoint operators
  Jun 2024, CIRM Luminy (FR)
  Powers of discrete Laplacians and Hardy-type inequalities

• 7th Najman Conference on Spectral Theory and Differential Equations
  Sep 2023, Brijuni (HR)
  Powers of discrete Laplacians and Hardy-type inequalities

• Workshop Differential-Algebraic Equations and Operator Pencils
  Apr 2023, Banff International Research Station (CA)
  Dominant Schur complements

• Nov 2022, Graz University of Technology (AT)
  An improved discrete Rellich inequality on the half-line

• Functional analysis, operator theory and dynamical systems seminar
  Nov 2022, Online Seminar University of Leipzig / Potsdam (DE)
  An improved discrete Rellich inequality on the half-line

• Workshop IX Partial differential equations, optimal design and numerics
  Aug 2022, Centro de Sciencias de Benasque Pedro Pascual (ES)
  Schur complement dominance with applications to damped wave equations

• May 2022, Vienna University of Technology (AT)
  The pseudo numerical range

• Apr 2022, Czech Technical University in Prague (CZ)
  Schur complement dominance with applications to wave equations and Dirac operators

• Nov 2020, Queen's University Belfast (UK)
  Spectrum of the Ekman boundary layer problem

• Mar 2018, University of Bern (CH)
  Holomorphic families and spectral inclusion

Teaching

Czech Technical University in Prague 2023

• Calculus II

Queen's University Belfast 2019 - 2020

• Numbers, Vectors and Matrices

University of Bern 2017 - 2020

• Operator Theory

• Advanced Analysis

• Functional Analysis

• Ordinary Differential Equations

• Mathematics in Economy and Social Sciences I, II

• Mathematics in Biology I

Vienna University of Technology 2010 - 2012

• Analysis II, III

• Mathematics in Engineering I, II

Employment

2024 - currently MSCA fellow at the Institute of Science and Technology Austria (AT) under supervision of Prof. R. Seiringer

2022 - 2024 postdoc of Prof. D. Krejčiřík at the Czech Technical University in Prague (CZ) within EXPRO grant of the Czech National Science Foundation

Education

2021 - PhD degree in Mathematics (supervised by C. Tretter), University of Bern (CH)

2019 - SEMP research internship, Queen's University Belfast (UK)

2016 - Master's degree in Technical Mathematics, Vienna University of Technology (AT)

2014 - Erasmus student exchange, Université Paris Dauphine (FR)

2012 - Bachelor's degree in Technical Mathematics, Vienna University of Technology (AT)